The numerical initial boundary value problem for the generalized conformal field equations

In this paper we study a numerical implementation for the initial boundary value formulation for the generalized conformal field equations. We propose a formulation which is well suited for the study of the long-time behaviour of perturbed exact solutions such as a Schwarzschild or even a Kerr black...

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Bibliographic Details
Published in:arXiv.org 2017-08
Main Authors: Beyer, Florian, Frauendiener, Jörg, Stevens, Chris, Whale, Ben
Format: Article
Language:English
Subjects:
Boundary conditions
Boundary value problems
Gravitation
Minkowski space
Relativity
Spacetime
Well posed problems
Online Access:Get full text
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Summary:In this paper we study a numerical implementation for the initial boundary value formulation for the generalized conformal field equations. We propose a formulation which is well suited for the study of the long-time behaviour of perturbed exact solutions such as a Schwarzschild or even a Kerr black hole. We describe the derivation of the implemented equations which we give in terms of the space-spinor formalism. We discuss the conformal Gauss gauge, and a slight generalization thereof which seems to be particularly useful in the presence of boundaries. We discuss the structure of the equations at the boundary and propose a method for imposing boundary conditions which allow the correct number of degrees of freedom to be freely specified while still preserving the constraints. We show that this implementation yields a numerically well-posed system by testing it on a simple case of gravitational perturbations of Minkowski space-time and subsequently with gravitational perturbations of Schwarzschild space-time.
ISSN:2331-8422
DOI:10.48550/arxiv.1706.01416